Several constructions for factorization systems

Dali Zangurashvili

The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) `reflects' factorization systems. In particular, a generalization of the well-known Cassidy-Héebert-Kelly factorization theorem is given. The problem of relating a factorization system to a pointed endofunctor is considered. Some relevant examples in concrete categories are given.

Keywords: (local) factorization system, family of adjunctions between slice categories, semi-left-exact reflection, fibration, (co)pointed endofunctor

2000 MSC: 18A20, 18A32, 18A25

Theory and Applications of Categories, Vol. 12, 2004, No. 11, pp 326-354.

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